Question

A dart hits the circular dartboard shown below at a random point. Find the probability that the dart lands in the shaded square region. The radius of the dartboard is 9

in, and each side of the shaded region is 3in.

Answer 1

$Total~area= Area ~of~ the ~bigger ~circle= Ac= \pi*(radiu~of~the~dashboard)^2 = 3.14 * 9^2=254.34 ~square~in.$

$Desired~area=(Area~of~the~shaded~smaller)^2= As = 3^2=9~square~in.$

$Then~Geometric~Probability= \frac{ Area ~of~ the ~shaded ~smaller~ square}{Area~ of ~the~ bigger ~circle}= \cfrac {As}{Ac}= \cfrac {9}{254.34}= 0.0354$

Answer: 0.0354